Find the principal value of each of the following:
(i) `sin^(-1)((sqrt(3)+1)/(2sqrt(2)))`
(ii) `sin^(-1)(cos(3pi)/4)`
(iii) `sin^(-1)(tan(5pi)/4)`

Explanation

To find the principal value of each of the given expressions, we will break down the calculations step by step.

### (i) Find `sin^(-1)((sqrt(3)+1)/(2sqrt(2)))`

1. **Simplify the expression**:
\[ \frac{\sqrt{3}+1}{2\sqrt{2}} = \frac{\sqrt{3}}{2\sqrt{2}} + \frac{1}{2\sqrt{2}} = \frac{\sqrt{3}}{2} \cdot \frac{1}{\sqrt{2}} + \frac{1}{2} \cdot \frac{1}{\sqrt{2}} \]
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